Normal Surface Singularities

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Normal Surface Singularities

Author : András Némethi
Publisher : Springer Nature
ISBN 13 : 3031067533
Total Pages : 732 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Normal Surface Singularities by : András Némethi

Download or read book Normal Surface Singularities written by András Némethi and published by Springer Nature. This book was released on 2022-10-07 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a comprehensive introduction to the theory of complex normal surface singularities, with a special emphasis on connections to low-dimensional topology. In this way, it unites the analytic approach with the more recent topological one, combining their tools and methods. In the first chapters, the book sets out the foundations of the theory of normal surface singularities. This includes a comprehensive presentation of the properties of the link (as an oriented 3-manifold) and of the invariants associated with a resolution, combined with the structure and special properties of the line bundles defined on a resolution. A recurring theme is the comparison of analytic and topological invariants. For example, the Poincaré series of the divisorial filtration is compared to a topological zeta function associated with the resolution graph, and the sheaf cohomologies of the line bundles are compared to the Seiberg–Witten invariants of the link. Equivariant Ehrhart theory is introduced to establish surgery-additivity formulae of these invariants, as well as for the regularization procedures of multivariable series. In addition to recent research, the book also provides expositions of more classical subjects such as the classification of plane and cuspidal curves, Milnor fibrations and smoothing invariants, the local divisor class group, and the Hilbert–Samuel function. It contains a large number of examples of key families of germs: rational, elliptic, weighted homogeneous, superisolated and splice-quotient. It provides concrete computations of the topological invariants of their links (Casson(–Walker) and Seiberg–Witten invariants, Turaev torsion) and of the analytic invariants (geometric genus, Hilbert function of the divisorial filtration, and the analytic semigroup associated with the resolution). The book culminates in a discussion of the topological and analytic lattice cohomologies (as categorifications of the Seiberg–Witten invariant and of the geometric genus respectively) and of the graded roots. Several open problems and conjectures are also formulated. Normal Surface Singularities provides researchers in algebraic and differential geometry, singularity theory, complex analysis, and low-dimensional topology with an invaluable reference on this rich topic, offering a unified presentation of the major results and approaches.

Singularities and Their Interaction with Geometry and Low Dimensional Topology

Author : Javier Fernández de Bobadilla
Publisher : Springer Nature
ISBN 13 : 3030619583
Total Pages : 332 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Singularities and Their Interaction with Geometry and Low Dimensional Topology by : Javier Fernández de Bobadilla

Download or read book Singularities and Their Interaction with Geometry and Low Dimensional Topology written by Javier Fernández de Bobadilla and published by Springer Nature. This book was released on 2021-05-27 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is a collection of surveys and original research articles concentrating on new perspectives and research directions at the crossroads of algebraic geometry, topology, and singularity theory. The papers, written by leading researchers working on various topics of the above fields, are the outcome of the “Némethi60: Geometry and Topology of Singularities” conference held at the Alfréd Rényi Institute of Mathematics in Budapest, from May 27 to 31, 2019. Both the conference and this resulting volume are in honor of Professor András Némethi, on the occasion of his 60th birthday, whose work plays a decisive and influential role in the interactions between the above fields. The book should serve as a valuable resource for graduate students and researchers to deepen the new perspectives, methods, and connections between geometry and topology regarding singularities.

Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities

Author : William Gignac
Publisher : American Mathematical Society
ISBN 13 : 1470449587
Total Pages : 100 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities by : William Gignac

Download or read book Local Dynamics of Non-Invertible Maps Near Normal Surface Singularities written by William Gignac and published by American Mathematical Society. This book was released on 2021-11-16 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.

Deformations of Surface Singularities

Author : Andras Némethi
Publisher : Springer Science & Business Media
ISBN 13 : 3642391311
Total Pages : 280 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Deformations of Surface Singularities by : Andras Némethi

Download or read book Deformations of Surface Singularities written by Andras Némethi and published by Springer Science & Business Media. This book was released on 2014-01-24 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present publication contains a special collection of research and review articles on deformations of surface singularities, that put together serve as an introductory survey of results and methods of the theory, as well as open problems and examples. The aim is to collect material that will help mathematicians already working or wishing to work in this area to deepen their insight and eliminate the technical barriers in this learning process. Additionally, we introduce some material which emphasizes the newly found relationship with the theory of Stein fillings and symplectic geometry. This links two main theories of mathematics: low dimensional topology and algebraic geometry. The theory of normal surface singularities is a distinguished part of analytic or algebraic geometry with several important results, its own technical machinery, and several open problems. Recently several connections were established with low dimensional topology, symplectic geometry and theory of Stein fillings. This created an intense mathematical activity with spectacular bridges between the two areas. The theory of deformation of singularities is the key object in these connections.

Normal Two-Dimensional Singularities. (AM-71), Volume 71

Author : Henry B. Laufer
Publisher : Princeton University Press
ISBN 13 : 1400881749
Total Pages : 176 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Normal Two-Dimensional Singularities. (AM-71), Volume 71 by : Henry B. Laufer

Download or read book Normal Two-Dimensional Singularities. (AM-71), Volume 71 written by Henry B. Laufer and published by Princeton University Press. This book was released on 2016-03-02 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: A survey, thorough and timely, of the singularities of two-dimensional normal complex analytic varieties, the volume summarizes the results obtained since Hirzebruch's thesis (1953) and presents new contributions. First, the singularity is resolved and shown to be classified by its resolution; then, resolutions are classed by the use of spaces with nilpotents; finally, the spaces with nilpotents are determined by means of the local ring structure of the singularity.

Resolution of Surface Singularities

Author : Vincent Cossart
Publisher : Springer
ISBN 13 : 3540391258
Total Pages : 138 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Resolution of Surface Singularities by : Vincent Cossart

Download or read book Resolution of Surface Singularities written by Vincent Cossart and published by Springer. This book was released on 2006-11-14 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Topological Methods in Algebraic Geometry

Author : Friedrich Hirzebruch
Publisher : Springer
ISBN 13 : 3662306972
Total Pages : 241 pages
Book Rating : 4.6/5 (623 download)

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Book Synopsis Topological Methods in Algebraic Geometry by : Friedrich Hirzebruch

Download or read book Topological Methods in Algebraic Geometry written by Friedrich Hirzebruch and published by Springer. This book was released on 2013-11-11 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Lipschitz Geometry of Singularities

Author : Walter Neumann
Publisher : Springer Nature
ISBN 13 : 3030618072
Total Pages : 356 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Introduction to Lipschitz Geometry of Singularities by : Walter Neumann

Download or read book Introduction to Lipschitz Geometry of Singularities written by Walter Neumann and published by Springer Nature. This book was released on 2021-01-11 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a broad overview of the important recent progress which led to the emergence of new ideas in Lipschitz geometry and singularities, and started to build bridges to several major areas of singularity theory. Providing all the necessary background in a series of introductory lectures, it also contains Pham and Teissier's previously unpublished pioneering work on the Lipschitz classification of germs of plane complex algebraic curves. While a real or complex algebraic variety is topologically locally conical, it is in general not metrically conical; there are parts of its link with non-trivial topology which shrink faster than linearly when approaching the special point. The essence of the Lipschitz geometry of singularities is captured by the problem of building classifications of the germs up to local bi-Lipschitz homeomorphism. The Lipschitz geometry of a singular space germ is then its equivalence class in this category. The book is aimed at graduate students and researchers from other fields of geometry who are interested in studying the multiple open questions offered by this new subject.

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Author : Sirakov Boyan
Publisher : World Scientific
ISBN 13 : 9813272899
Total Pages : 5396 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Sirakov Boyan

Download or read book Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) written by Sirakov Boyan and published by World Scientific. This book was released on 2019-02-27 with total page 5396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

Arc Schemes And Singularities

Author : David Bourqui
Publisher : World Scientific
ISBN 13 : 1786347210
Total Pages : 312 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis Arc Schemes And Singularities by : David Bourqui

Download or read book Arc Schemes And Singularities written by David Bourqui and published by World Scientific. This book was released on 2020-03-05 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This title introduces the theory of arc schemes in algebraic geometry and singularity theory, with special emphasis on recent developments around the Nash problem for surfaces. The main challenges are to understand the global and local structure of arc schemes, and how they relate to the nature of the singularities on the variety. Since the arc scheme is an infinite dimensional object, new tools need to be developed to give a precise meaning to the notion of a singular point of the arc scheme.Other related topics are also explored, including motivic integration and dual intersection complexes of resolutions of singularities. Written by leading international experts, it offers a broad overview of different applications of arc schemes in algebraic geometry, singularity theory and representation theory.

Milnor Fiber Boundary of a Non-isolated Surface Singularity

Author : András Némethi
Publisher : Springer
ISBN 13 : 3642236472
Total Pages : 240 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Milnor Fiber Boundary of a Non-isolated Surface Singularity by : András Némethi

Download or read book Milnor Fiber Boundary of a Non-isolated Surface Singularity written by András Némethi and published by Springer. This book was released on 2012-01-05 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of algebraic/analytic varieties a key aspect is the description of the invariants of their singularities. This book targets the challenging non-isolated case. Let f be a complex analytic hypersurface germ in three variables whose zero set has a 1-dimensional singular locus. We develop an explicit procedure and algorithm that describe the boundary M of the Milnor fiber of f as an oriented plumbed 3-manifold. This method also provides the characteristic polynomial of the algebraic monodromy. We then determine the multiplicity system of the open book decomposition of M cut out by the argument of g for any complex analytic germ g such that the pair (f,g) is an ICIS. Moreover, the horizontal and vertical monodromies of the transversal type singularities associated with the singular locus of f and of the ICIS (f,g) are also described. The theory is supported by a substantial amount of examples, including homogeneous and composed singularities and suspensions. The properties peculiar to M are also emphasized.

Resolution of Curve and Surface Singularities in Characteristic Zero

Author : K. Kiyek
Publisher : Springer Science & Business Media
ISBN 13 : 9781402020285
Total Pages : 522 pages
Book Rating : 4.0/5 (22 download)

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Book Synopsis Resolution of Curve and Surface Singularities in Characteristic Zero by : K. Kiyek

Download or read book Resolution of Curve and Surface Singularities in Characteristic Zero written by K. Kiyek and published by Springer Science & Business Media. This book was released on 2004-10 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the beautiful theory of resolutions of surface singularities in characteristic zero. The primary goal is to present in detail, and for the first time in one volume, two proofs for the existence of such resolutions. One construction was introduced by H.W.E. Jung, and another is due to O. Zariski. Jung's approach uses quasi-ordinary singularities and an explicit study of specific surfaces in affine three-space. In particular, a new proof of the Jung-Abhyankar theorem is given via ramification theory. Zariski's method, as presented, involves repeated normalisation and blowing up points. It also uses the uniformization of zero-dimensional valuations of function fields in two variables, for which a complete proof is given. Despite the intention to serve graduate students and researchers of Commutative Algebra and Algebraic Geometry, a basic knowledge on these topics is necessary only. This is obtained by a thorough introduction of the needed algebraic tools in the two appendices.

Real and Complex Singularities

Author : Terence Gaffney
Publisher : American Mathematical Soc.
ISBN 13 : 082183665X
Total Pages : 338 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Real and Complex Singularities by : Terence Gaffney

Download or read book Real and Complex Singularities written by Terence Gaffney and published by American Mathematical Soc.. This book was released on 2004 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Workshop on Real and Complex Singularities is held every other year at the Instituto de Ciencias Matematicas e de Computacao (Sao Carlos, Brazil) and brings together specialists in the vanguard of singularities and its applications. This volume contains articles contributed by participants of the seventh workshop. The included papers reflect Fields Medalist Rene Thom's original vision of singularities and represent all branches of the subject: equisingularity of sets and mappings, the geometry of singular complex analytic sets, singularities of mappings and their elimination, characteristic classes, applications to differential geometry, differential equations, and bifurcation theory. The book is suitable for graduate students and researchers interested in singularity theory.

Singularities - Kagoshima 2017: Proceedings Of The 5th Franco-japanese-vietnamese Symposium On Singularities

Author :
Publisher : World Scientific
ISBN 13 : 981120604X
Total Pages : 312 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Singularities - Kagoshima 2017: Proceedings Of The 5th Franco-japanese-vietnamese Symposium On Singularities by :

Download or read book Singularities - Kagoshima 2017: Proceedings Of The 5th Franco-japanese-vietnamese Symposium On Singularities written by and published by World Scientific. This book was released on 2020-06-15 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a proceedings of the 5th Franco-Japanese-Vietnamese Symposium on Singularities held in Kagoshima during 27th October - 3rd November, 2017. The main theme of the symposium was Singularity Theory in a broad sense, including complex and real algebraic varieties, functions and mappings, and topology of singularities. The symposium was based on long-term interaction of singularity theorists in France, Japan, Vietnam and other countries. This volume includes three surveys of recent trends based on the lectures in the mini-school organized in the first two days of the symposium and articles presenting recent progress in Singularity Theory.

Singularities and Computer Algebra

Author : Wolfram Decker
Publisher : Springer
ISBN 13 : 3319288296
Total Pages : 389 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Singularities and Computer Algebra by : Wolfram Decker

Download or read book Singularities and Computer Algebra written by Wolfram Decker and published by Springer. This book was released on 2017-03-29 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book arose from a conference on “Singularities and Computer Algebra” which was held at the Pfalz-Akademie Lambrecht in June 2015 in honor of Gert-Martin Greuel’s 70th birthday. This unique volume presents a collection of recent original research by some of the leading figures in singularity theory on a broad range of topics including topological and algebraic aspects, classification problems, deformation theory and resolution of singularities. At the same time, the articles highlight a variety of techniques, ranging from theoretical methods to practical tools from computer algebra.Greuel himself made major contributions to the development of both singularity theory and computer algebra. With Gerhard Pfister and Hans Schönemann, he developed the computer algebra system SINGULAR, which has since become the computational tool of choice for many singularity theorists.The book addresses researchers whose work involves singularity theory and computer algebra from the PhD to expert level.

Handbook of Geometry and Topology of Singularities III

Author : José Luis Cisneros-Molina
Publisher : Springer Nature
ISBN 13 : 3030957608
Total Pages : 822 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Handbook of Geometry and Topology of Singularities III by : José Luis Cisneros-Molina

Download or read book Handbook of Geometry and Topology of Singularities III written by José Luis Cisneros-Molina and published by Springer Nature. This book was released on 2022-06-06 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third volume of the Handbook of Geometry and Topology of Singularities, a series which aims to provide an accessible account of the state of the art of the subject, its frontiers, and its interactions with other areas of research. This volume consists of ten chapters which provide an in-depth and reader-friendly survey of various important aspects of singularity theory. Some of these complement topics previously explored in volumes I and II, such as, for instance, Zariski’s equisingularity, the interplay between isolated complex surface singularities and 3-manifold theory, stratified Morse theory, constructible sheaves, the topology of the non-critical levels of holomorphic functions, and intersection cohomology. Other chapters bring in new subjects, such as the Thom–Mather theory for maps, characteristic classes for singular varieties, mixed Hodge structures, residues in complex analytic varieties, nearby and vanishing cycles, and more. Singularities are ubiquitous in mathematics and science in general. Singularity theory interacts energetically with the rest of mathematics, acting as a crucible where different types of mathematical problems interact, surprising connections are born and simple questions lead to ideas which resonate in other parts of the subject, and in other subjects. Authored by world experts, the various contributions deal with both classical material and modern developments, covering a wide range of topics which are linked to each other in fundamental ways. The book is addressed to graduate students and newcomers to the theory, as well as to specialists who can use it as a guidebook.

Singularities

Author : Peter Orlik
Publisher : American Mathematical Soc.
ISBN 13 : 0821814508
Total Pages : 676 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Singularities by : Peter Orlik

Download or read book Singularities written by Peter Orlik and published by American Mathematical Soc.. This book was released on 1983 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: On April 7-10, 1980, the American Mathematical Society sponsored a Symposium on the Mathematical Heritage of Henri Poincari, held at Indiana University, Bloomington, Indiana. This title presents the written versions this Symposium. It contains two papers by invited speakers who were not able to attend, S S Chern and L Nirenberg.